cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A372444 The n-th iterate of 27 with A371094.

Original entry on oeis.org

27, 165, 8021, 12408149, 19607957362005, 32439509492992549521282389, 58947232705679751034215288252890081792789279233365, 259166427025070423330595967015238989905128148712607202753574381749095993394717720069452733214971221
Offset: 0

Views

Author

Antti Karttunen, May 01 2024

Keywords

Crossrefs

Cf. A371094.
Column 7 of A371102, column 14 of A372282.
Column 1 of A372560.
Sequences derived from this one:
A372443 obtained when Reduced Collatz-function R is applied to a(n-1), for n > 0,
A372445 column index of a(n) in array A257852,
A372448 the 2-adic valuation of 1 + 3*a(n), equal to row index of a(n) in array A257852,
A372449 binary lengths minus 1; their first differences: A372451,
A372452 number of terms of A086893 in the interval [a(n), a(1+n)],
A372454 the difference between a(n) and the term of A086893 with the same binary length.

Programs

  • PARI
    A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
    A372444(n) = { my(x=27); while(n, x=A371094(x); n--); (x); };

Formula

a(0) = 27; for n > 0, a(n) = A371094(a(n-1)).

A372452 Number of terms of A086893 in the interval [A372444(n), A372444(1+n)].

Original entry on oeis.org

2, 6, 10, 21, 41, 80, 162, 324, 646, 1294, 2586, 5173, 10345, 20691, 41381, 82760, 165522, 331044, 662089, 1324177, 2648353, 5296707, 10593413, 21186827, 42373652, 84747305, 169494609, 338989216, 677978435, 1355956869, 2711913736, 5423827472, 10847654948, 21695309896, 43390619791, 86781239586, 173562479173, 347124958344
Offset: 0

Views

Author

Antti Karttunen, May 05 2024

Keywords

Comments

The formula involving A372451 and A372453 shows that each term is at most +-1 from the corresponding term of A372451, that are the first differences of A372449.

Examples

			Between A372444(0)=27 and A372444(1)=165 there are two terms (53 and 85) of A086893, therefore a(0) = 2.
Between A372444(1)=165 and A372444(2)=8021 there are six terms (213, 341, 853, 1365, 3413, 5461) of A086893, therefore a(1) = 6.
Between A372444(2)=8021 and A372444(3)=12408149 there are 10 terms (13653, 21845, 54613, 87381, 218453, 349525, 873813, 1398101, 3495253, 5592405) of A086893, therefore a(2) = 10.
		

Crossrefs

Programs

Formula

a(n) = A372286(A372444(n)).
a(n) = A372451(n) + [A372453(n)<=0] - [A372453(1+n)<0], where [ ] is the Iverson bracket, yielding 1 or 0 depending on whether the given inequivalence holds or does not hold.
Showing 1-2 of 2 results.